Question

What is the price of a European call option on a non-dividend-paying stock when the stock price is $102, the strike price is $100, the risk-free interest rate is 8% per annum, the volatility is 35% per annum, and the time to maturity is six months using BSM model. work the problem out do not use excel

Answer 1

S = stock price = 102

X = exercise price = 100

r = Risk free interest rate =8% = 0.08

t = time of expiration = 6months = 6/12 = 0.5

Standard deviation (Volatility) =35% =0.35

Calculation of price of European call option:

Step- 1: Log(S/X) = Log(102/100) = Log(1.02) = 0.01980

Step-2:d1=Log(S/X)+(square of volatility/2+r)*t/volatility*square root of t

= 0.01980+((0.35*0.35)/2+0.08)*0.5/0.35*square root of 0.5

= 0.01980+0.070625/0.2475

=0.090425/0.2475

=0.36

Step-3: d2 = d1-volatility*Square root of t

=0.3653-0.2475

=0.12

Step 4 : N(d1) = N(0.36) = 0.6406

Step 5: N(d2) = N(0.12) = 0.5478

Step 6:

Price = S*N(d1)-X*e-rt*N(d2)

(*Calculation of e-0.08*0.5= e-0.04= (1+0.04/1+0.04*0.04/2)= 1+0.04+0.0008 = 1.0408 =1.041 (appoxiamately))

= 102*0.6406-100*e-0.08*0.5*0.5478

= 65.3412-100/1.041*0.5478

=65.3412-52.6224

=12.7188

Approxiamately 13

Price of European Call option = 13

*Values of N(d1) and N(d2) we can find out using standard statistical table.